Getting on the London Under­ground with my dog, Missy, is a bit of a nightmare. That is not because she is scared of the roar of the trains, or because she finds the crowds intimidating – quite the opposite. Missy always bounds enthusiastically into the carriage and proceeds to waggle her hindquarters at the nearest commuter. It does not occur to her that the bleary passengers may not be in the mood to fuss over her, much less that some of them may not like dogs full-stop. Even if the train is standing room only, she is still quite relaxed, flopping down on top of polished brogues and suede stilettos, her tail draped across a briefcase or curling around an umbrella. I, meanwhile, tense with embarrassment, frantically but ineffectually twitch her lead in an effort to steer her clear of anyone who sidles away or frowns.

Missy is what a dog trainer would call “well socialised”. In part, that is because she is a cockerpoo, an innately friendly breed. In part, that is because my wife and I, never having owned a dog before and scared witless by the how-to manuals’ blood-curdling tales of adorable puppies growing into vicious, misanthropic recluses, went to great lengths to introduce her to crowds of strangers before she reached 12 weeks. (After that, the most forbidding dog-rearing book warned, it would be “too late”.) But I can’t help thinking that Missy is also the canine equivalent of a Jehovah’s Witness, eagerly accosting every passer-by, thanks to BorrowMyDoggy, a dog-sharing service we use.

For those whose schedules make it hard to pay their dog enough attention, outfits like BorrowMyDoggy are a godsend. They match owners, who need someone to stop Fido getting so bored he chews the skirting boards and pees on the sofa, with people who volunteer to walk or dogsit lonely pooches because they want the fun of having a dog to play with occasionally without the hassle and expense of owning one full-time.

In London, in particular, flats are small and landlords often insert no-pet clauses into leases as boilerplate. But the city’s hip, knowledge-economy companies are happy to let employees work from home or keep them on such irregular schedules that squeezing in an afternoon or two of dog-minding a week is easy. This mutually satisfactory model is spreading: Canada has a service called Part-time Pooch and Australia has one called Dogshare.

But I can’t help feeling a twinge of jealousy every time Missy prances out the door with another helpful borrower. This being London, the volunteers are from all over: India, New Zealand, Poland, Sweden – even the odd Brit. Some take her to the park, some to their flats and some to their offices, where a whole new crowd of strangers is waiting to fawn over her. Missy has been gallivanting off like this since she was a small puppy; she is now a seven-month-old adolescent. She is so comfortable with new people that she would be no use at all as a guard dog. The only danger she would pose to a burglar would be to follow him around the house so closely that he might trip up.

Alexandra Horowitz, who teaches canine psychology at Columbia University in New York, says this is perfectly normal. Most of the world’s dogs, she points out, are strays living in the developing world. Their natural habitat, as it were, is the proximity of humans, but they do not have a specific owner. Instead, they attach themselves temporarily to whoever is nice to them.

There is good evidence that dogs form genuine attachments to humans, and can become depressed when these bonds of affection are sundered. But they need not be exclusive. As Roger Mugford, an animal psychologist who helped to train the queen’s corgis, puts it, “You can overplay the idea of loyalty to the last gasp.”

Of course, the disloyalty can run both ways. Gavin Flett, who founded Part-time Pooch, is too busy studying and running a startup to keep a dog of his own. But his family had a dog when he was little, and whenever life calms down, he plans to get one again. In the meantime, he regularly uses his own service to borrow one of two different dogs. After all, he points out, if he borrowed just one, he couldn’t count on it to be available when he was in the mood for canine companionship. Now I own one dog, I find myself curious about others. What would it be like, I wonder, to have a sheepdog or a chihuahua for a day?